1. Field of the Invention
This invention relates to electronic circuits, and more particularly, the design of power distribution systems.
2. Description of the Related Art
As computer system technology advances, there is a continuous demand for systems that demand higher power at a relatively low voltage. Designing power distribution systems that can deliver a large amount of current at low voltages is a significant challenge. Tight voltage tolerances (e.g. xc2x15%) are often times required to ensure the proper performance of silicon chips within a computer system. The lower operating voltages may result in much lower target impedance requirements. At the same time, the clock frequencies at which microprocessors and other types of silicon chips operate are continually increasing, thereby resulting in a much wider frequency range for which target impedance requirements must be met.
Power distributions systems typically include at least one pair of planar conductors (e.g. a power plane and a ground plane), separated by a dielectric layer. A plurality of capacitors may be electrically connected in a parallel configuration between the planar conductors in order to provide a low impedance path for power distribution. Many power distribution systems employ a plurality of ceramic capacitors mounted upon a printed circuit board (PCB). Such capacitors may be chosen based on their ability to meet target impedance requirements for a given frequency. Capacitors having different electrical characteristics may be chosen to meet the target impedance requirements over a wide frequency range.
Electrical characteristics of capacitors which must be considered when designing power distribution systems include capacitance, equivalent series resistance (ESR) and equivalent series inductance (ESL). These characteristics have a significant effect on the electrical response of a given capacitor over a frequency range. At lower frequencies, the impedance provided by a capacitor is dominated by its capacitance. Since capacitors include conductive elements, such as conductive plates and mounting pads or pins, there is an inductance (ESL) associated with them. This inductance dominates the impedance profile of a capacitor at higher frequencies. The point at which the inductive and capacitive reactances cancel each other out is known as the resonant frequency, and the impedance provided by the capacitor at this frequency (which is purely resistive) is known as the ESR.
FIG. 1 illustrates the frequency response for a typical capacitor. At lower frequencies, the impedance decreases with frequency at a rate of approximated xe2x88x9220 dB/decade. At these frequencies, the impedance provided by the capacitor is dominated by capacitance, and may be calculated by the formula       Z    =          1              j        ⁢                  xe2x80x83                ⁢        ω        ⁢                  xe2x80x83                ⁢        C              ,
where Z is the impedance, C is the capacitance, and xcfx89 is the angular frequency. As frequency increases, the capacitor will eventually achieve a state of resonance, as the capacitive reactance will be offset by the inductive reactance. This resonant frequency, sometimes referred to as the series resonant frequency, may be calculated by the formula       F    =          1              2        ⁢        π        ⁢                  LC                      ,
where F is the resonant frequency, L is the equivalent series inductance, and C is the capacitance. The impedance provided by a capacitor at its resonant frequency is the capacitor""s ESR. At frequencies above the resonant frequency, the impedance provided by a capacitor may be dominated by its ESL. The impedance of the capacitor for frequencies greater than the resonant frequency may be calculated by the formula
Z=jxcfx89L, 
where Z is the impedance, L is the ESL, and xcfx89 is the angular frequency. In designing power distribution systems, a plurality of capacitors having different impedance profiles may be combined in order to achieve a target impedance over a wide frequency range.
Designing power distribution systems and determining the necessary decoupling capacitors may include a significant amount of modeling and simulation. The power distribution system, as well as the various circuitry to which power is to be provided, may be modeled and simulated so as to predict the performance of the power distribution system under various operating conditions.
Performance prediction using modeling and simulation may include determining the effects of certain resonances that may affect power distribution system operation. These resonances may be associated with the parallel plate geometry of the power planes, and may have significant effect on the performance of the power distribution system if not accounted for during the design phase. In particular, there are two types of resonances that typically must be addressed in order to design a power distribution system that is effectively decoupled over a wide frequency bandwidth. One of these types of resonances is known as LC (inductive-capacitive) resonance. LC resonance may result from the inter-plane capacitance (i.e. the capacitance existing between the power and ground planes, including any capacitors electrically coupled between these planes) resonating with the inductance of the mounted decoupling capacitors. LC resonance may result in one or more impedance peaks at frequencies about the series resonant frequency.
The other type of resonance that must be managed is known as cavity resonance. Cavity resonances may be a function of the dimensions (x-y) and geometry of the circuit board or carrier of the power distribution system and the various frequencies of the system (i.e. clock frequencies and associated harmonics). In particular, the relationship between the dimensions of the circuit board and the wavelengths of the various frequencies present may cause impedance peaks and valleys to occur at various physical positions on the board itself. These positions may be located at distances that are multiples of xc2xc wavelength, xc2xd wavelength, {fraction (3/2)} wavelengths, and so on, from the edge of the circuit board. Standing waves at these positions may result in either impedance peaks or impedance valleys. The high impedance peaks, if left unchecked, may result in excess noise in the power distribution system, and may also be problem frequencies for electromagnetic interference (EMI).
Managing both the LC and cavity resonances may be affected by the manner in which the power distribution system and its various components are modeled, as well as the order in which the resonances are dealt with during the design phase. However, it is important that impedance peaks resulting from both of these types of resonance be damped in order to meet target impedance requirements across a wide range of frequencies.
FIGS. 2 and 3 may illustrate the effects of one method of modeling capacitors. FIG. 2 is a schematic of one embodiment of a traditional electrical model for a capacitor. The embodiment shown is a model of a capacitor based on a series RLC circuit. The model includes a resistor representing the capacitor""s ESR value, a capacitor representing its capacitance value, and an inductor representing its ESL value. The model may be implemented as a SPICE model or other type of mathematical for simulation on a computer system.
The capacitor model of FIG. 2 may be useful for simulation at lower frequencies, but may be inadequate for higher frequencies. As previously stated, power distribution systems typically include a pair of planar conductors separated by a dielectric, which may act as a capacitor at lower frequencies. At higher frequencies, a pair of planar conductors may develop the impedance resonances discussed above. Impedance peaks resulting from these resonances are sometimes referred to as anti-resonances, or parallel resonances. The traditional series RLC circuit model of a capacitor may be unable to correctly predict the frequency or frequencies at which anti-resonances occur.
FIG. 3 is a graph illustrating the simulated and measured performance of a capacitor mounted between two power planes over a range of frequencies, wherein the simulation is based on the traditional model of FIG. 2. Both the simulated and measured results were for a pair of conductive planes (i.e. a power plane and ground plane) having a single capacitor mounted and electrically connected between the planes. The capacitor model used for the simulated results was the traditional RLC series circuit model. As can be seen from examining the graph, model-to-hardware correlation is good for the lower frequencies. However, the simulated results differ from the measured results significantly with respect to both the frequency and magnitude of the first anti-resonant peak. In this particular example, the simulated results predict an anti-resonant peak at a lower frequency and of significantly higher magnitude than that obtained by the measured results. Second and third anti-resonant peaks also differ between simulated and measured results. The second anti-resonant peak from the measured results occurs at a frequency close to that which is predicted by the simulated results. The third anti-resonant peak for the measured results occurs at a higher frequency and lower magnitude than predicted by the simulated results.
In addition to the problems inherent in the modeling as discussed above, the order in which the various resonances are dealt with may also complicate the design problem. Attempts to suppress impedance peaks induced by LC resonance may result in the changing of behavior of the cavity resonances. In particular, the peaks associated with cavity resonances may change frequency as the result of the suppression of impedance peaks resulting from LC resonances. The shifting frequency of the cavity resonance peaks may in turn lead to changing locations of the poles and zeros of the system when analysis is performed in the frequency domain. Thus, the problems of predicting the amplitude and frequency of anti-resonant peaks resulting from the modeling may be further aggravated by the shifting of anti-resonant peaks resulting from one type of resonance when attempting to manage another type of resonance.
A methodology for determining the placement of decoupling capacitors in a power distribution system and system therefor is disclosed. In one embodiment, a method for determining the placement of decoupling capacitors in a power distribution system includes determining a target impedance, creating a power distribution system model, performing an LC (inductive-capacitive) resonance analysis, and performing a cavity resonance analysis. During the performance of the LC resonance analysis, capacitors may be selected in order to suppress impedance peaks resulting from LC resonances. Following the LC resonance analysis, the method may place the capacitors in the power distribution system at evenly spaced intervals. During the performance of the cavity resonance analysis, the capacitors may be repositioned in the power distribution system so as to suppress cavity resonances.
In one embodiment, performing the LC resonance analysis may include a single node analysis of the capacitors selected for the power distribution system. Following an initial selection of decoupling capacitors, a system for performing the method may simulate the capacitors as being connected in parallel. The simulation may further include injecting a signal at a node where the capacitors are electrically coupled and sweeping the signal across a frequency range of interest. Following the sweeping of the signal, a comparison of the measured impedance at one or more frequencies with the target impedance may be performed, with special attention paid to any anti-resonant impedance peaks that may be present. The methodology may then repeat the selecting of capacitors, which may include adding capacitors to the system and/or selecting capacitors having different electrical characteristics. Following the repeating of the capacitor selection, the methodology may again simulate the injection of a signal and the sweeping across a frequency range. This iterative process may continue until the impedance peaks are all suppressed to a level at or below the target impedance. When the measured impedance (sometimes referred to as the transfer impedance) is below the target impedance for all required frequencies, the method may place the capacitors in the power distribution system at evenly spaced intervals.
Performing the cavity resonance analysis may include simulating the injection of a signal at a predetermined node in the power distribution system, sweeping the signal across a frequency range, and analyzing the results at a plurality of nodes. In one embodiment, the power distribution system may be modeled by an Mxc3x97N grid having a plurality of cells connected at predetermined nodes. The signal may be injected at any of these nodes, while the analysis may be performed at any or all of the predetermined nodes. The analysis may include comparing the transfer impedance measured at each of the predetermined nodes to the target impedance for one or more frequencies. The analysis may further include determining the frequency and physical location within the power distribution system where impedance peaks may occur. In response to determining the frequency and physical location of an impedance peak, a nearby capacitor having a series resonant frequency that is approximately the same as the frequency of the impedance peak may be moved to or near that physical location in order to suppress the peak. This may be followed by repeating the injection of the signal and sweeping it across the frequency range. The method of cavity resonance analysis may undergo a number of iterations, repositioning capacitors until all impedance peaks resulting from cavity resonances are suppressed to a level at or below the target impedance. In one embodiment, the iterative process may begin by addressing the impedance peaks occurring at the lowest frequencies first and then progressively addressing the peaks at higher frequencies. This iterative process may continue until all of the peaks are sufficiently suppressed and that the transfer impedances is at or below the target impedance for all measured frequencies.
In one embodiment, a computer system may be configured to perform the method responsive to executing instructions stored on a carrier medium. The computer system may include one or more output devices for displaying the results of the methodology to a user. The user may also be able to view intermediate results through one of the output devices. Results obtained from performing the method may be presented by any suitable method of presentation, including the presentation of graphical results or tabulated results.